In how many ways can $5$ red and $4$ white balls be drawn from a bag containing $10$ red and $8$ white balls?

At an election,a voter may vote for any number of candidates not exceeding the number to be elected. If $4$ candidates are to be elected out of the $12$ contested in the election and a voter votes for at least one candidate,then the number of ways in which a voter can vote is:

If $\alpha = \binom{m}{2}$,then $\binom{\alpha}{2} = \dots$

The number of ways to distribute $25$ identical apples among $4$ boys,such that each boy receives at least $4$ apples,is

In how many ways can a committee of $5$ members be formed from $6$ men and $4$ women such that the committee contains at least one woman?

If $^{43}C_{r-6} = ^{43}C_{3r+1}$,then the value of $r$ is